This paper is concerned with the practical complexity of the symbolic computation of limit cycles associated with Hilbert’s 16th problem. In particular, in determining the number of small-amplitude limit cycles of a non-linear dynamical system, one often faces computing the focus values of Hopf-type critical points and solving lengthy coupled polynomial equations. These computations must be car...

In the present paper a realization of a classical method for Lyapunov quantities computation in Maple is considered. Key–Words: Lyapunov quantity, focus values, symbolic computation, small-amplitude limit cycles, Maple, Hilbert 16th problem

where f (x, y) and g(x, y) are real polynomials of x and y with degree not greater than n, 1h is an oval lying on real algebraic curve H(x, y)=h, deg H(x, y)=m (H(x, y) are called Hamiltonians), and 7 is a maximal interval of existence of 1h . This question is called the weakened Hilbert 16th problem, posed by V.I. Arnold in [1, 2]. The general result of solving the weakened Hilbert 16th proble...

This paper discusses concepts of command for complex endeavors. The traditional concepts of Unity of Command and Unity of Effort are found wanting, the former because there is no single individual in command of a complex endeavor, the latter because there is often no time to develop the comprehensive plan required, and if there is time, it is nevertheless difficult because different organizatio...

Architecture frameworks have become a popular means to cope with the complexity of today’s enterprises. They support the specification of architectures by providing a method for designing and describing them. An architecture framework typically defines a common terminology, a set of views focusing on particular aspects of the architecture, a set of architecture types with varying levels of deta...

Effective Command and Control (C2) is enabled by information technology, but the potential of C2 through virtual environments offers opportunities for radical increases in awareness and performance. To realize such radical increases, we are engaged in a campaign of experimentation to assess C2 in virtual environments through the ELICIT (Experimental Laboratory for Investigating Collaboration, I...